Environment plays a pivotal role in shaping the evolution of satellite galaxies. Analysing the properties related to the cold gas phase of satellites provides insights into unravelling the complexity of environmental effects. We use the hydro-dynamical simulations the IllustrisTNG project and the EAGLE simulations, and the semi-analytic models (SAMs) GAlaxy Evolution and Assembly (GAEA) and L-Galaxies, in comparison with recent observations from the Westerbork Synthesis Radio Telescope, to investigate the properties of satellite galaxies hosted by haloes with mass M-200 > 10(12.8) M-circle dot, and within projected regions <= 1.1 virial radius R-200. Generally, satellite galaxies selected from semi-analytic models have more HI than those selected from hydro-dynamical simulations across all projected radii, e.g. more than 30 percent of satellites in the two hydro-simulations are HI depleted, while this fraction is almost zero in SAMs. Furthermore, both hydro-dynamical simulations and SAMs reproduce the observed decrease of HI content and specific star formation rate towards the halo centre. However, the trend is steeper in two hydro-dynamical simulations TNG and EAGLE, resulting in a better agreement with the observational data, especially in more massive haloes. By comparing the two version of GAEA, we find that the inclusion of ram-pressure stripping of cold gas significantly improves the predictions on HI fractions. The refined hot gas stripping method employed in one of the two L-Galaxies models also yields improved results.